Method to measure electrophoretic mobility of a flowing sample

ABSTRACT

When measuring electrophoretic mobility it is customary to apply an electric field and determine the electrophoretic velocity while minimizing all other contributions to the particle movement. A method and apparatus for the measurement of mobility while the sample is flowing is disclosed. Combined with a fractionation system, this approach further enables the direct measurement of individual species&#39; mobility within a multi-modal sample. Other advantages of this new mobility measurement approach include the ability to easily pressurize the sample to suppress electrolysis, mitigation of oxidation-reduction effects and efficient heat dissipation.

PRIORITY

This application is a continuation of U.S. patent application Ser. No.15/521,255, filed Apr. 21, 2017, and claims priority to U.S. Provisionalapplication No. 62/076,366, filed Nov. 6, 2014, and to PCT ApplicationNo. PCT/US2015/059419, filed Nov. 6, 2015.

BACKGROUND

The invention discloses an innovative method and apparatus by which themotion of charged particles in a solution subject to an applied electricfield may be measured. Although the present invention will refer tomacromolecules throughout much of its specification, the inventionincludes more generally all classes of small particles includingemulsions, viruses, nanoparticles, liposomes, macro-ions and any othersolution constituents whose size may lie between a half and a fewthousand nanometers. Thus whenever the terms “molecule,”“macromolecule,” or “macro-ion” are used, it should be understood theyinclude all of the aforementioned solution-borne objects.

Electrophoretic mobility is widely accepted as a sensitive probe ofinterfacial charge, and it has found numerous applications in bothbiological and colloidal samples. The correlation betweenelectrophoretic mobility and colloidal stability, formulation stabilityand inter-molecular interactions has been and remains a subject ofactive research.

Electrophoresis is the migration of macro-ions under the influence of anelectric field. A steady-state electrophoretic velocity, v_(e), attainedby the migrating macro-ions is linearly proportional to the appliedelectric field. When a field is applied, the molecules' velocities areessentially always in equilibrium. To measure electrophoretic mobility,an electric field E is applied to drive electrophoresis of chargedspecies, whose velocity v_(e) is then measured to determine theelectrophoretic mobility through the relationship

v _(e) =μE  (1)

where μ is the electrophoretic mobility, or the velocity per unitelectric field. An objective of the present invention is to provide animproved method for the measurement of the electrophoretic mobility ofparticles in solution.

Several techniques have been developed and are available for measuringelectrophoretic mobility. Among these techniques are the moving boundarymethod, microelectrophoresis, and electrophoretic light scattering, ELS,which includes several light scattering methods including heterodynedynamic light scattering, DLS, laser Doppler electrophoresis, LDE, andphase analysis light scattering, PALS. The electrophoretic mobility canalso be measured by an electroacoustic means: electrokinetic sonicamplitude, ESA, as described by Oja, et. al. in U.S. Pat. No. 4,497,208,Issued Feb. 5, 1985, “Measurement of Electro-Kinetic Properties of aSolution.”

Free-solution measurements of electrophoretic mobility have beenroutinely carried out in the batch mode wherein a sample containingmacromolecules of interest is loaded into an apparatus, an AC(alternating current) electric field is applied and the electrophoreticvelocity is directly measured without externally imposed flow

In general, the movement of macromolecules can be diffusional, due toBrownian motion, and collective, due to electro-osmosis,electrophoresis, externally applied fluid flow, thermal convection, etc.In order to determine the electrophoretic component, the contributionsto molecular motions from other mechanisms must be accounted for. Thecontribution from random Brownian motion is necessarily averaged outover multiple measurements. The effects of electro-osmosis can beignored by measuring at the stationary layer, or by increasing thefrequency of electric field reversal to suppress electro-osmosis. Thecontribution from thermal convection or residual bulk fluid flow can besubtracted out since it is independent of the direction of the appliedelectric field and shows up as a constant velocity component while theelectrophoretic component switches polarity in synchronicity with thealternating electric field. Most instruments are able to account forthermal convection that is usually the undesirable byproduct ofelectrical currents. When it comes to the measurement of electrophoreticmobility, the conventional wisdom states that such measurements shouldbe performed under minimum bulk fluid flow. A volume flow rate 0.2mL/min or higher can easily overwhelm the mobility measurements.

A BRIEF DESCRIPTION OF THE INVENTION

In this application, we proposed an apparatus that facilitates flow-modemeasurements of the electrophoretic mobility. The externally imposedflow naturally constitutes a means for introducing and extruding thesample of interest. The flow adds a constant velocity component to themacromolecular motion on top of the field-driven electrophoresis. Solong as this flow velocity component is correctly subtracted out, themobility measurement can be successfully made. We will discuss theinnovative elements that make this operation possible and greatly extendthe upper limit of the volume flow rate. Although PALS is taken as ourprimary method of measuring electrophoretic mobility and used in ourillustrations, it should be understood that these innovations can beapplied to other means of electrophoretic mobility measurement.

A BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a phase diagram for light scattering. An electric field Ealong the x-axis is applied to drive electrophoresis.

FIG. 2 illustrates the direction of fluid flow parallel to thepropagation of the laser beam minimizing the associated Doppler/phasecomponent in the low scattering angles.

FIG. 3 shows a chromatogram of a mixture of proteins: thyroglobulin,bovine serum albumin (BSA) and carbonic anhydrase separated by SEC.

A DETAILED DESCRIPTION OF THE INVENTION

There are many great advantages to measuring electrophoretic mobility inthe flow mode, that is while a sample flows through a measurement cell,as opposed to the batch, or stop-flow-mode, discussed previously. Amongthese advantages are real time, online measurement of electrophoreticmobility, constant solvent exchange mitigating the effects ofoxidation/reduction reactions, pressurization of the measurement cellwhich can mitigate bubbles within the cell itself, and efficient heatdissipation.

The ability to resolve multiple species' electrophoretic mobilities in agiven sample is often desirable. In batch-mode measurements, if thesample contains multiple species with distinct electrophoreticmobilities, the measured mobility will be some weighted average of allspecies' mobilities. In light scattering measurements, such as ELS, LDEor PALS, the measured mobility is the intensity-weighted average.Fourier analysis has been applied to resolve multiple mobility speciesin ELS, but the resolution of such multimodal analysis is limited inpractice, most likely because of the inherent dual (size and mobility)polydispersity. The situation gets even more challenging whenmacromolecules smaller than about 20 nm are of interest, due toincreased diffusional broadening in the power spectrum of the scatteredsignal.

Flow-mode mobility measurement can be directly coupled with numerousfractionation techniques to characterize the electrophoretic mobility ofeach eluted species separately. The mobility can therefore be measured“on-line”. Size-exclusion chromatography, ion-exchange chromatography,and field-flow fractionation are just a few of the possibilities. Inaddition to being much more robust than numerical multimodal analyses,the on-line measurement of electrophoretic mobility provides extrainformation through the physiochemical parameters upon which thechemical species are fractionated. For example, size-exclusionchromatography fractionates based on the sample hydrodynamic volume.Furthermore, other sample parameters of interest, such as theconcentration and hydrodynamic radius of each species, can be measured,either simultaneously or subsequently, to increase the utility of such asystem. The hydrodynamic radius is a necessary parameter for thecalculation of molecular charge in the Debye-Hückle-Henry model.

It is worth noting that capillary electrophoresis, CE, a well-knownhigh-resolution separation technique, can be used for the separation ofcharged macromolecules based on electrophoretic mobility. In capillaryzone electrophoresis, CZE, electro-osmotic flow typically dominates allelectrophoretic components and all charged species are swept towards thecathode, with cations reaching the detector earlier and anions later.The electrophoretic mobility of each charged species can be computedfrom the time it takes for each species to reach the detector with theelectro-osmotic component corrected out. To characterize theelectro-osmosis, a neutral marker is necessary. However, even with aneutral marker, sample interaction with the capillary wall can never beruled out and the measured electrophoretic mobility can be inaccurate.On the other hand, a free-solution technique is free of suchnon-idealities.

In addition to online mobility measurement, flow-mode mobilitymeasurement has another interesting advantage: It mitigates the effectsof reduction-oxidation, also known as redox, reactions. Mobilitymeasurements are inherently perturbing due to the applied electricfield/current. Redox reactions take place on the electrodes' surface andthe macromolecular mobility can be altered either through directmodification of the macromolecular oxidation state (chemical damage) orindirect modulation by the accompanying change of buffer state (pH,ionic species, etc.). Flow-mode operation delivers a constant freshsupply of sample and buffer that greatly decreases the effects of theinevitable redox products in conductive samples.

Yet another advantage of flow-mode mobility measurement is the ease withwhich the measurement volume can be pressurized to avoid gas bubblesarising from electrolysis. The sample cell of a flow-mode mobilityapparatus is necessarily enclosed and leak-proof up to a certain fluidpressure. A back-pressure regulator can be connected downstream from thesample cell to provide pressurization of the sample being measured. Thisis especially valuable when the sample contains high concentrations ofsalts (e.g., physiological saline) or when the gas evolution due to theensuing electrolysis can affect the mobility measurements. Utilizationof a downstream back-pressure regulator enables the sample-deliveringflow to double as a means to pressurize the sample.

Passing electric current through conductive samples inevitably generatesheat. Depending on the conductivity of the sample, its temperature canincrease appreciably by this heat generation. An increased temperaturecan affect mobility measurements by changing the solution viscosity.Some degree of sample degradation can also be caused by an elevatedtemperature. A constant flow efficiently carries off the excess heat tomaintain the temperature of the sample being measured.

It is therefore highly desirable to be able to measure electrophoreticmobility in flow-mode, yet several impediments have heretofore made anysuch measurements impractical. However the method and apparatusdescribed herein allows flow-mode measurements by employing severalnovel enhancements to traditional systems.

To begin with, the design of the sample cell of any measurementinstrument plays an important role in facilitating flow-modemeasurements and achieving the full potential of the advantages. Theinstruments ability to properly account for the effects of a constantflow is essential to successfully measuring electrophoretic mobility inflow mode. In PALS measurements, macromolecular electrophoresisgenerates phase variations that are measured interferometrically todetermine electrophoretic mobility, see, for example U.S. Pat. No.8,441,638 issued May 14, 2013, by Trainoff and Hsieh, “Method andapparatus to measure particle mobility in solution with scattered andunscattered light,” hereby incorporated by reference. Bulk sample flowcan confound the measurements if its component along the scatteringvector is excessive. As shown in FIG. 1, the sample is subjected to aflow velocity v_(c) and an electric field E is applied to driveelectrophoresis. The collective sample velocity, v_(c), can include allcollective motions which are uncorrelated with the electric field, e.g.,fluid convection. Also shown are the wave vectors of the incident light,and the scattered light, k_(s). The scattering vector q_(s) is definedas q_(s)=k_(s)−k_(i). The Doppler shift (or optical phase change perunit time) due to macromolecular electrophoresis is equal tof_(E)=μq_(s)·E; this quantity is measured to determine theelectrophoretic mobility μ. On the other hand, the sample flow atvelocity v_(c) also generates its associated Doppler shiftf_(c)=q_(s)·v_(c). Since the flow velocity v_(c) does not changedirection with the alternating electric field, the two Doppler shiftcomponents, f_(E) and f_(c), can in general be separated and themobility can be determined.

However, depending on the sample electrophoretic mobility, system designand flow rate, the component f_(c)=q_(s)·v_(c)=q_(s)v_(c)=q_(s)v_(c) cosϕ can grow much larger than f_(E)=μq_(s)·E=q_(s)E cos(θ_(s)/2) and startto affect the mobility measurements. A good system and flow cell designshould maximize the Doppler shift f_(E) from electrophoresis whileminimizing the Doppler component f_(c) from the fluid flow. This can beachieved by having the electric field E roughly parallel to thescattering vector q_(s) and the collective flow direction roughlyperpendicular to the scattering vector, i.e. ϕ≈90°.

FIG. 2 illustrates the elements of a specialized flow cell and assemblyfor measurement of electrophoretic mobility based on PALS. To minimizethe component f_(c), the fluid inlet 201 and outlet 202 of the flow cell203 are positioned such that the fluid flow 204 direction is essentiallyparallel to the direction of the laser beam 205 path and perpendicularto the electric field direction generated by the electrodes 206. Theflow direction is also roughly perpendicular to the scattering vector atlow scattering angles of less than about 15°. With detectors covering arange of scattering angles θ_(s) between about 4° and 15°, thecorresponding range of the angle ϕ is between about 88° and 82.5°. As aresult the component f_(c) is effectively suppressed, cos ϕ<<1. On theother hand, the direction of the electric field E is roughly parallel tothe scattering vector q_(s), maximizing the Doppler component f_(E) dueto electrophoresis, cos(θ_(s)/2)≈1.

The majority of the instruments for electrophoretic mobilitymeasurements have designs wherein the electric field, scattering vectorand the “would-be” flow direction are all roughly parallel to oneanother. Such a configuration not only renders the mobility measurementsmore susceptible to thermal convection effects, but also greatly limitstheir ability to carry out meaningful measurements when any fluid flowis present.

If a mobility measurement cell is to be used in flow mode, it is also arequirement that the sample chamber be leak-proof since the flow-modeoperation is most often implemented with a fluid pump serving as meansof sample delivery, and any restrictions on the fluid beyond the samplechamber itself will generate a back pressure in the measurement cell. Nosuch requirement for the capacity to withstand significant fluidpressure is required in, for example, mobility measurement systems whichmake use of cuvettes. Therefore, any measurement cell designed to beused in flow mode should be leak proof, preferably capable of sustaininga back pressure of 50 bars or more.

A sample cell designed with backpressure in mind offers an additionalbenefit to the inventive method and apparatus disclosed herein. Such adesign facilitates the pressurization of the sample chamber. Theoperator of the system, or the system design itself, can simply connecta back-pressure regulator at the outlet of the flow cell to apply astable back pressure on the sample being measured. This mode ofoperation is especially advantageous when the sample contains highconcentrations of salts such as those of physiological saline or higher.Such pressurization is also beneficial as gas evolution due toelectrolysis, to which electrophoretic mobility measurements havetraditionally been extremely susceptible, can adversely affect themobility measurements.

As discussed above, the management of flow is extremely important to thesuccessful operation of any flow-mode measurement of electrophoreticmobility. But as the flow rate increases, the flow will eventuallyintroduce enough phase shift per unit time (i.e., Doppler frequencyshift f_(c)) to confound the mobility measurement. These deleteriouseffects on measurement due to fluid flow begin when the actual phaseshift introduced by the flow is more than π or less than −π betweensuccessive phase measurements. Under these circumstances, aliasingoccurs and erroneous measurements of the mobility are obtained.Instruments with only one detector are especially vulnerable to thistype of phase-unwrapping error because they cannot correctly detect theactual phase in this case and will “alias” the phase difference up ordown modulo 2π. There is no additional information available to correctfor this eventuality in a single-detector mobility measurement system.

The novel solution to the problems associated with measurement ofmobilities in a flowing disclosed herein comprise the utilization ofmultiple detectors corresponding to a range of scattering angles in theapparatus. In the absence of phase-unwrapping errors, such as, at alower fluid flow rate, the phase shift attributable to the fluid flow,measured by the i-th detector, is the inner product q_(si)·v_(c), whereq_(si) is the scattering vector corresponding to the i-th detector. Aglobal fit across all the detectors yields the fluid flow direction andvelocity. In the presence of phase unwrapping errors, cross-checking thephase shifts measured by the detectors will overcome this abnormalityand restore the actual phase shift to (still) accurately recover theflow direction and velocity. This greatly extends the range of usableflow rate and the instrument's capability to carry out flow-modeelectrophoretic mobility measurements.

One preferred embodiment of the inventive apparatus employs 31 detectorscovering arrange of scattering angles from 4° to 15°. A volume flow rateof 1.0 mL/min results in a flow velocity of approximately 10 mm/s in thecenter of the cell where the mobility measurements are taken. (Since thechannel flow profile resembles Poiseuille flow, the average flowvelocity is approximately 5 mm/s.) When the phase measurements are madeat 1 kHz, phase unwrapping errors start at a flow rate of 1.0 mL/min forthe highest angle. Without performing a global fit to the multipleangles, this would be the upper limit of the compatible flow rate. Notethat due to the optimized flow cell of this preferred embodiment, thislimit is already at least an order of magnitude higher than aconventional design where the would-be flow direction is perpendicularto the laser propagation. An upper flow rate limit of 1.0 mL/min iseasily compatible with most HPLC and/or fractionation techniques. With31 detectors, the upper limit may be extended to a flow rate beyond 40mL/min.

Demonstration of Method

To demonstrate the feasibility of online flow-mode electrophoreticmeasurements as disclosed herein, the novel system is connecteddownstream from a size-exclusion chromatography, SEC, column with fluidflow rate passing there through of 0.2 mL/min. The sample used in thisexample was a mixture of three proteins, all obtained fromSigma-Aldrich, Co., St. Louis, Mo. The samples were thyroglobulin,bovine serum albumin and carbonic anhydrase. The proteins were preparedin a 10 mM sodium chloride and 10 mM phosphate buffer saline with a pHof 7.0. The same buffer served as the mobile phase of the chromatographysystem. The resulting chromatogram, shown in FIG. 3, was recorded by aninline refractive index, RI, detector (Optilab T-rEX, Wyatt TechnologyCorporation, Santa Barbara, Calif.). The three well-separated majorpeaks representing the monomers of the proteins are clearly seen in thechromatogram as thyroglobulin 301, bovine serum albumin 302 and carbonicanhydrase 303.

Electrophoretic mobilities of the three proteins were measured in threedifferent ways. First a mixture of all three proteins was prepared inthe buffer and measured online after passing through the SEC column. Theproteins were measured again after being prepared individually in thesame buffer and measured online after passing through an SEC column.Lastly, the three proteins were measured individually in the batch mode.The results are summarized in Table 1. Since the apparatus also measuresthe translational diffusion coefficient, the computed hydrodynamic radiiare shown along with the measured electrophoretic mobilities. Allaverages and standard deviations are calculated based on thirty 6-secondmeasurements. In the flow mode, we select for consideration the regionof the peak which is 70% of the maximum concentration of the peak.

TABLE 1 Flow mode (Online) Mixture of proteins Individual proteininjections Batch Mode measurements Mobility Hydrodynamic MobilityHydrodynamic Mobility Hydrodynamic Sample (μm · cm/V · s) Radius (nm)(μm · cm/V · s) Radius (nm) (μm · cm/V · s) Radius (nm) Thyroglobulin−1.56 ± 0.06 8.70 ± 0.15 −1.59 ± 0.10 8.73 ± 0.13 −1.48 ± 0.10 9.40 ±0.08 Bovine Serum −1.03 ± 0.08 3.48 ± 0.09 −1.04 ± 0.09 3.46 ± 0.05−1.09 ± 0.09 3.56 ± 0.01 Albumin Carbonic −0.41 ± 0.07 2.42 ± 0.04 −0.42± 0.09 2.40 ± 0.04 −0.82 ± 0.05 2.64 ± 0.03 Anhydrase

Note that all online measurements of electrophoretic mobility resultsagree well regardless of whether the proteins were injected individuallyor injected onto the column as a mixture. This indicates that theproteins are well separated by the chromatography system andconsistently measured by the apparatus. SEC fractionates based onmacromolecular hydrodynamic volume, and the measured hydrodynamic radiicorroborate proper fractionation. The slight discrepancies between thebatch-mode and flow-mode measurements for thyroglobulin and bovine serumalbumin can be attributed to the sample polydispersity. Thyroglobulinhas a monomer content of approximately 80% mass ratio and bovine serumalbumin contains a 3% mass ratio of various oligomers. This can bemeasured by the RI detector and the oligomer peak 304 associated withthe bovine serum albumin can be seen in the chromatograph of FIG. 3. Thebatch-mode vs. flow-mode measurements of carbonic anhydrase do not agreeas well and this is most likely due to a much lower monomer content ofapproximately 55% mass ratio, also measured by the RI detector. Themeasurements of hydrodynamic radii also confirmed the samplepolydispersity in the batch measurements.

The results summarized in Table 1 demonstrate the utility offlow-mode/online measurements when the bulk flow is properly accountedfor. The flow-mode/online operation benefits from the fractionationmethod's ability to resolve multiple species in a polydisperse sample,and can achieve resolution impossible for the batch-mode operation toattain.

As will be evident to those skilled in the arts of light scattering,macromolecular characterization, and electrophoretic mobilitymeasurements, there are many obvious variations of the methods anddevices of our invention that do not depart from the fundamentalelements that we have listed for their practice; all such variations arebut obvious implementations of the invention described hereinbefore andare included by reference to our claims, which follow.

What is claimed is:
 1. A method comprising: flowing a sample solutioncomprising particles through a sample cell comprising a measurementchamber configured to allow the sample solution to flow in a directionessentially parallel to a path of a laser beam transmitted through themeasurement chamber, a fluid inlet coupled to the measurement chamberand configured to introduce the sample solution into the measurementchamber, and a fluid outlet coupled to the measurement chamber andconfigured to allow the sample solution to exit the measurement chamber;and generating, via electrodes, an alternating electric field across themeasurement chamber and essentially perpendicular to the direction;fractionating the sample solution; and measuring a concentration of eachspecies in the sample solution, resulting in a measured concentration ofthe each species in the sample solution.
 2. The method of claim 1wherein the fractionating comprises fractionating the sample solutionvia a field flow fractionation system.
 3. The method of claim 1 whereinthe fractionating comprises fractionating the sample solution via a sizeexclusion chromatography system.
 4. The method of claim 1 wherein themeasuring comprises measuring the concentration via a refractive indexdetector.
 5. The method of claim 1 further comprising measuring ahydrodynamic radius of the each species in the sample solution,resulting in a measured hydrodynamic radius of the each species in thesample solution.
 6. The method of claim 5 further comprising calculatinga molecular charge of the each species in the sample solution withrespect to the measured concentration and the measured hydrodynamicradius.